Multi-dimensional Fourier Transform (FT) NMR spectroscopy is broadly used in chemistry (Ernst et al., “Principles of Nuclear Magnetic Resonance in One and Two Dimensions,” Oxford: Oxford University Press (1987); Jacobsen, N. E., “NMR Spectroscopy Explained,” Wiley, New York (2007)) and spectral resolution is pivotal for its performance. The use of forward and backward sampling for pure absorption mode signal detection to obtain improved spectral resolution is described in Bachman et al., J. Mag. Res., 28:29-39 (1977), however, this methodology does not allow phase-sensitive detection. In particular, Bachmann et al. teach the combined forward-backward sampling of a chemical shift evolution along one axis, the ‘x-axis’, only. This results in two cosine modulations which, after addition, yield a real time domain signal devoid of terms that lead to dispersive components in the frequency domain spectrum obtained after a cosine transformation. Hence, Bachmann et al. do not teach phase-sensitive detection of chemical shifts.
Phase-sensitive, pure absorption mode signal detection (Ernst et al., “Principles of Nuclear Magnetic Resonance in One and Two Dimensions,” Oxford: Oxford University Press (1987); Cavanagh et al., “Protein NMR Spectroscopy,” 2nd Ed., San Diego Academic Press (2007); Schmidt-Rohr et al., “Multidimensional Solid-State NMR and Polymers,” New York: Academic Press (1994)) is required for achieving high spectral resolution since an absorptive signal at frequency Ω0 rapidly decays proportional to 1/(Ω0−Ω)2 while a dispersive signal slowly decays proportional to 1/(Ω0−Ω). Hence, a variety of approaches were developed to accomplish pure absorption mode signal detection (Ernst et al., “Principles of Nuclear Magnetic Resonance in One and Two Dimensions,” Oxford: Oxford University Press (1987); Cavanagh et al., “Protein NMR Spectroscopy,” 2nd Ed., San Diego: Academic Press (2007); Schmidt-Rohr et al., “Multidimensional Solid-State NMR and Polymers,” New York: Academic Press (1994)). Moreover, by use of techniques such as spin-lock purge pulses (Messerle et al., J. Magn. Reson. 85:608-613 (1989)), phase cycling, (Ernst et al., “Principles of Nuclear Magnetic Resonance in One and Two Dimensions,” Oxford: Oxford University Press (1987)) pulsed magnetic field gradients, (Keeler et al., Methods Enzymol. 239:145-207 (1994)) or z-filters (Sorensen et al., J. Magn. Reson. 56:527-534 (1984)), radio-frequency (r.f.) pulse sequences for phase-sensitive detection are designed to avoid ‘mixed’ phases, so that only phase errors remain which can then be removed by a zero-or first-order phase correction.
A limitation of the hitherto developed approaches (Ernst et al., “Principles of Nuclear Magnetic Resonance in One and Two Dimensions,” Oxford: Oxford University Press (1987); Cavanagh et al., “Protein NMR Spectroscopy,” 2nd Ed., San Diego: Academic Press (2007); Schmidt-Rohr et al., “Multidimensional Solid-State NMR and Polymers,” New York: Academic Press (1994)) arises whenever signals exhibit phase errors which cannot be removed by a zero-or first-order correction, or when aliasing limits (Cavanagh et al., “Protein NMR Spectroscopy,” 2nd Ed., San Diego: Academic Press (2007)) first-order phase corrections to 0° or 180°. Due to experimental imperfections, such phase errors inevitably accumulate to some degree during the execution of r.f. pulse sequences (Ernst et al., “Principles of Nuclear Magnetic Resonance in One and Two Dimensions,” Oxford: Oxford University Press (1987); Cavanagh et al., “Protein NMR Spectroscopy,” 2nd Ed., San Diego: Academic Press (2007); Schmidt-Rohr et al., “Multidimensional Solid-State NMR and Polymers,” New York: Academic Press (1994)) which results in superposition of the desired absorptive signals with dispersive signals of varying relative intensity not linearly correlated with Ω0. This not only exacerbates peak identification, but also reduces the signal-to-noise (S/N) and shifts the peak maxima. In turn, this reduces the precision of chemical shift measurements and impedes spectral assignment based on matching of shifts.
Furthermore, phase-sensitive, pure absorption mode detection of signals encoding linear combinations of chemical shifts relies on joint sampling of chemical shifts as in Reduced-dimensionality (RD) NMR (Szyperski et al., J. Am. Chem. Soc. 115:9307-9308 (1993); Brutscher et al., J. Magn. Reson., B109:238-242 (1995); Szyperski et al., Proc. Natl. Acad. Sci. USA 99:8009-8014 (2002)) and its generalization, G-matrix Fourier transform (GFT) projection NMR (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003); Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004); Xia et al., J. Biomol. NMR 29:467-476 (2004); Eletsky et al., J. Am. Chem. Soc. 127, 14578-14579 (2005); Yang et al., J. Am. Chem. Soc. 127:9085-9099 (2005); Atreya et al., Methods Enzymol. 394:78-108 (2005); Liu et al., Proc. Natl. Acad. Sci. U.S.A. 102:10487-10492 (2005); Atreya et al., J. Am. Chem. Soc. 129:680-692 (2007)). The latter is broadly employed, in particular also (Szyperski et al., Magn. Reson. Chem. 44:51-60 (2006)) for projection-reconstruction (PR) (Kupce et al., J. Am. Chem. Soc. 126:6429-6440 (2004); Coggins et al., J. Am. Chem. Soc. 126:1000-1001 (2004)), high-resolution iterative frequency identification (HIFI) (Eghbalnia et al., J. Am. Chem. Soc. 127:12528-12536 (2005)), and automated projection (APSY) NMR (Hiller et al., Proc. Natl. Acad. Sci. U.S.A. 102:10876-10881 (2005)). Importantly, the joint sampling of chemical shifts entangles phase errors from several shift evolution periods. Hence, zero-and first-order phase corrections cannot be applied in the GFT dimension (Atreya et al., J. Am. Chem. Soc. 129:680-692 (2007)), which further accentuates the need for approaches which are capable of eliminating (residual) dispersive components.
In Atreya et al., J. Am. Chem. Soc. 129:680-692 (2007), measurement of nuclear spin-spin coupling is taught. In particular, Atreya et al. teach transforming a secondary phase shift in the cosine J-modulation arising from ‘J-mismatch’, that is, variation of J by spins system requiring different Δt=½J delays for each spin system, into an imbalance of amplitudes of sine and cosine modulation. This yields quadrature image peaks which are not removed. Atreya et al. teach combined forward and backward sampling of cosine modulations, since sine modulations are not affected by secondary phase shifts arising from J-mismatch.
The present invention is directed to overcoming these and other deficiencies in the art.